Question

So I need a little help with these 2 problems of my homework.

Answer 1

To find the slope for these cases, we need to take two points or coordinates, and then use the slope formula:

`m=(y_2-y_1)/(x_2-x_1)`

In the first graph, we have the next two points:

(2, 12) and (4, 16)

We have:

x1 = 2, y1 = 12

x2 = 4, y2 = 16

Then, the slope is:

`m=(16-12)/(4-2)\Rightarrow m=(4)/(2)\Rightarrow m=2`

We calculate the slope with the first two coordinates. This is the graph of the first case.

We need to find the equation of the line. For this, we have the slope, and we can take one pair of coordinates, and then use the Point-slope form of the line equation. Then, we have:

`y-y_1=m(x-x_1)\Rightarrow y-12=2(x-2)\Rightarrow y-12=2x-4`

Then, we have:

`y=2x-4+12\Rightarrow y=2x+8`

Then, the y-intercept is obtained when x = 0. If x =0, we have, from the equation that

y = 8. Therefore, the y-intercept is y = 8, that is, the line passes through this point in the y-axis.

The x-intercept is when we have that y = 0. In this case, we have:

`0=2x+8\Rightarrow2x=-8\Rightarrow x=(-8)/(2)\Rightarrow x=-4`

The graph for the line (first case) is: